RELAXED INERTIAL METHODS FOR SOLVING SPLIT VARIATIONAL INEQUALITY PROBLEMS WITHOUT PRODUCT SPACE FORMULATION

Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.

Effect of zirconium addition on the austenite grain coarsening behavior and mechanical properties of 900 MPa low carbon bainite steel

The ultra-fine bainitic microstructure of a 900 MPa low carbon bainitic Cu-Ni-Mo-B steel was obtained by a newly developed relaxation precipitation control （RPC） phase transformation processing. In a pan-cake like prior-austenite grain, the micro- structure consisted of lath bainite, a little of abnormal granular bainite, and acicular ferrite. The effect of zirconium carbonitrides on the austenite grain coarsening behavior was studied by transmission electron microscopy （TEM）. The results show that, the lath is narrower with increasing cooling rate. The ratio of all kinds of bainitic microstructure is proper with the intermediate cooling rate; and Zr-containing precipitates distribute uniformly, which restrains austenite grain growing in heat-affected welding zone.

A systematic literature review on the effectiveness of eurythmy therapy

BACKGROUND：Eurythmy therapy is a movement therapy of anthroposophic medicine that can have effects on a person’s physical body,spirit,and soul.OBJECTIVE：The aim of this publication was to update and summarize the relevant literature on the effectiveness of eurythmy in a therapeutic context since 2008.SEARCH STRATEGY：Different databases like Pub Med,MEDPILOT,Research Gate,The Cochrane Library,DIMDI,Arthe and also the journal databases Der Merkurstab and the European Journal of Integrative Medicine were searched for prospective and retrospective clinical trials in German or English language.INCLUSION CRITERIA：There were no limitations for indication,considered outcome or age of participants.DATA EXTRACTION AND ANALYSIS：Studies were evaluated with regard to their description of the assembly process and treatment,adequate reporting of follow-ups,and equality of comparison groups in controlled trials.RESULTS：Eleven studies met the inclusion criteria.These included two single-arm,non-controlled pilot studies,two publications on the same non-randomized controlled trial and one case study;six further studies referred to a prospective cohort study,the Anthroposophic Medicine Outcome Study.Most of these studies described positives treatment effects with varying effect sizes.The studies were heterogynous according to the indications,age groups,study design and measured outcome.The methodological quality of the studies varied considerably.There were no clear improvements since 2008,when the recommendations were published in the fi rst review.CONCLUSION：Eurythmy seems to be a benefi cial add-on in a therapeutic context that can improve the health conditions of affected persons.More methodologically sound studies are needed to substantiate this positive impression.